suggest how the ester might be separated from any unreacted ethanoic acid or methanol

Answer 1

Why not use a dehydrating agent, such as conc. sulfuric acid?

Answer 2

A sodium carbonate, Na2CO3, solution would neutralize ethanoic acid forming sodium acetate in the aqueous layer. A calcium chloride solution, CaCl2, would mix with the ethanol in the aqueous layer. Most of the ester would be in a separate layer on top of the water layer. The layers could be separated in a separatory funnel.